Collision bounds for 2D Sprites in the Blender Game Engine
Put your logic and physics settings on a different object, and parent your image plane to that object. Set your image plane as "no collision," and your other object's physics to "character." You can edit the collision bounds and other physics settings until you are happy with the result.

This is a setup I use commonly for making projectiles:



Here, I have a no collision plane parented to the collision object, but I am using rigid body physics instead of character physics on that actual physics object. - This would work in your case as well, just use character physics.